To solve the problem of subtracting the complex numbers [tex]\( (24 - 10i) - (43 + 18i) \)[/tex], let's break the problem into smaller, more manageable steps.
1. Identify the Real and Imaginary Parts:
- The first complex number [tex]\( 24 - 10i \)[/tex]:
- Real part: 24
- Imaginary part: -10
- The second complex number [tex]\( 43 + 18i \)[/tex]:
- Real part: 43
- Imaginary part: 18
2. Subtract the Real Parts:
[tex]\[
24 - 43 = -19
\][/tex]
3. Subtract the Imaginary Parts:
[tex]\[
-10 - 18 = -28
\][/tex]
4. Combine the Results:
- The real part of the result: [tex]\( -19 \)[/tex]
- The imaginary part of the result: [tex]\( -28 \)[/tex]
- Therefore, the result of the subtraction is:
[tex]\[
-19 - 28i
\][/tex]
5. Match the Result with the Given Options:
- Option A: [tex]\( -19 - 28i \)[/tex]
- Option B: [tex]\( 67 + 28i \)[/tex]
- Option C: [tex]\( -19 + 18i \)[/tex]
- Option D: [tex]\( -19 + 8i \)[/tex]
6. Select the Correct Option:
- Comparing the result [tex]\( -19 - 28i \)[/tex] with the options provided, we find that it matches Option A.
Therefore, the standard form of the complex number after the subtraction is:
[tex]\[
\boxed{-19 - 28i}
\][/tex]
